On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

Abstract

This paper is devoted to solving the output regulation problem on the basis of the new Francis equations for arbitrary reference/disturbance signals, whose model are obtained by High-Gain observers, providing in this way, the regulation of unmodeled but measurable reference signals. The design is given by fixing a steady state globally attractive by means of LMIs which allows controlling the decay rate by considering input bounds; while the regulation problem is solved by computing the steady-state input based on a modified set of the regulation equations, when the exosystem is constructed upon High-Gain observers, extending in this way, the classical output regulation theory for unmodeled reference/disturbance signal. The Furuta pendulum is used to illustrate the viability of the proposed approach.INDEX TERMS Output regulation, high-gain observer, linear matrix inequality.

The Output Regulation and the Kalman Filter as the Signal Generator

“…Thus, after solving the modified Francis equations derived in [8], [9] with A, B, and C given in Appendix A, one gets:…”

“…Therefore, if the reference/disturbance signals are measurable, but there is no exosystem to describe them, then the "classical" regulation theory cannot be used. This disadvantage has been partially overcome in [7], [8] and [9]. In [7], the authors use an extended High-Gain Observer (HGO) to estimate the states of the plant, the external disturbances, and the feedforward term necessary to track the reference.…”

“…In [7], the authors use an extended High-Gain Observer (HGO) to estimate the states of the plant, the external disturbances, and the feedforward term necessary to track the reference. Then, in [8], [9], the regulation theory is applied under the assumption that the reference/disturbance signals are nonmodeled but measurable for all t ≥ 0, smooth, and bounded, which allows a High-Gain Observer to be used as the exosystem. Also in [8], [9], the existence of the regulator was defined based on the solution of a modified set of Francis equations.…”

“…Then, in [8], [9], the regulation theory is applied under the assumption that the reference/disturbance signals are nonmodeled but measurable for all t ≥ 0, smooth, and bounded, which allows a High-Gain Observer to be used as the exosystem. Also in [8], [9], the existence of the regulator was defined based on the solution of a modified set of Francis equations.…”

“…To highlight the strengths and weaknesses of the proposed method, in this section, the exosystem is constructed using HGOs as in[8],[9]. For the sake of simplicity, each one of HGOs has dimension ρ = 2, and they are obtainedVOLUME 4, 2016 9 This article has been accepted for publication in IEEE Access.…”